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Abstract

A wavefront sensor has been used to measure the Kerr nonlinear focal shift of a high intensity ultrashort pulse beam in a focusing beam geometry while accounting for the effects of plasma-defocusing. It is shown that plasma-defocusing plays a major role in the nonlinear focusing dynamics and that measurements of Kerr nonlinearity and ionization are coupled. Furthermore, this coupled effect leads to a novel way that measures the laser ionization rates in air under atmospheric conditions as well as Kerr nonlinearity. The measured nonlinear index n2 compares well with values found in the literature and the measured ionization rates could be successfully benchmarked to the model developed by Perelomov, Popov, and Terentev (PPT model) [Sov. Phys. JETP 50, 1393 (1966)].

(a) Flat reference/initial wavefront recorded for the f/120 geometry at a beam energy of 0.3 mJ. The associated “defocus” term was measured at
R02=−0.005 waves. (b) Wave-front curvature recorded at 5.4 mJ energy with
R02=0.05 waves “defocus” for the same experimental configuration as (a).

Plot of the modeled laser beam waist versus propagation distance for the f/120 focusing geometry at various laser input energies. It can be seen that the waist moves towards the input optic as the laser beam energy increases. The geometrical focus is marked by the black dashed line. This is consistent with the experimental observation in Fig. 3. One can also see that the beam waist initially decreases as a function of self-focusing and later increases as plasma de-focusing sets in. The model parameters were as follows:wi = 6.2 mm, τ = 540 fs, λ = 1054 nm, NO2 = 4.6 × 1024 m−3 (accounting for 20% of O2 in the atmosphere and 85% of atmospheric pressure at the altitude of Albuquerque, NM), σ(K=11) = 3 × 10−191m22W−11s−1, and n2 = 2.6 × 10−23 m2/W.

Tables (1)

Table 1 Comparison of various values of n2 found in the literature. All values are in units of 10−23m2/W and correspond to atmospheric pressure. Note, reference [17] uses a 20 fs beam chirped to 200 fs.